A259758 - OEIS

A259758

Squarefree semiprimes of the form (2*p - 3) * (3*p - 2), p prime.

21, 91, 209, 589, 851, 2881, 7739, 10541, 16171, 26069, 29329, 75151, 95129, 110839, 165169, 194219, 216409, 220991, 264389, 374749, 411601, 653069, 717949, 829931, 1108969, 1119311, 1171741, 1269139, 1416689, 2059789, 3161729, 3374249, 3428459, 4924109

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = (2*A259730(n) - 3) * (3*A259730(n) - 2);

3431 = A033569(24) = (2*25-3)*(3*25-2) = 47*73 = A006881(946) is the smallest term in the intersection of A006881 and A033569 not belonging to this sequence.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 6*A259730(n)^2 - 13*A259730(n) + 6.

EXAMPLE

. n | p = A259730(n) | 2*p - 3 | 3*p - 2 | a(n)

. ----+----------------+---------+---------+--------

. 1 | 3 | 3 | 7 | 21

. 2 | 5 | 7 | 13 | 91

. 3 | 7 | 11 | 19 | 209

. 4 | 11 | 19 | 31 | 589

. 5 | 13 | 23 | 37 | 851

. 6 | 23 | 43 | 67 | 2881

. 7 | 37 | 71 | 109 | 7739

. 8 | 43 | 83 | 127 | 10541

. 9 | 53 | 103 | 157 | 16171

. 10 | 67 | 131 | 199 | 26069

. 11 | 71 | 139 | 211 | 29329

. 12 | 113 | 223 | 337 | 75151 .

MATHEMATICA

Select[Table[(2p-3)(3p-2), {p, Prime[Range[200]]}], PrimeOmega[#]==2&&SquareFreeQ[ #]&] (* Harvey P. Dale, Jul 20 2022 *)

PROG

(Haskell)

a259758 n = (2 * p - 3) * (3 * p - 2) where p = a259730 n

CROSSREFS

Cf. A259730, subsequence of A006881, subsequence of A033569.

Sequence in context: A284440 A020248 A225705 * A353056 A203173 A194532

Adjacent sequences: A259755 A259756 A259757 * A259759 A259760 A259761

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 05 2015

STATUS

approved